Origin of cosmic
magnetic fields

Keitaro Takahashi
Nagoya University, Japan

contents
1. Introduction
2. Magnetogenesis fromcosmological perturbations
3. Observation of tiny
cosmological B fields

1. Introduction

ubiquitous magnetic fields

neutronstar

1210 G
910 G

whitedwarf

610 G

activegalacticnuclei

310 G
Sun

1G
Earth

cluster ofgalaxies

1mG
SNR

1μG

galaxy

1km

6

10 km

1pc

1kpc

cosmological

1Mpc

size

cosmological magnetic field
big bang nucleosynthesis
B < 1 �G (Cheng et al. 96)
CMB anisotropy
B < 10 nG (Giovannini, Yamazaki et al.)Faraday rotation of distant radio sources
Bc < 0.1 nG (Vallee 90)

Do cosmological magnetic
fields exist?
SDSSmagnetogenesis
mechanisms
cosmological perturbation
KT et al. 05, 06, 07, 08
inflation
Turner & Widrow 88
Demozzi et al. 09
phase transition
Hogan 83
reionization
Langer et al. 03, 05

motivation
origin of magnetic fields
especially galaxies and clusters of galaxies
dynamo amplify tiny “seed” fields
where did the seed come from?
probe early universe
B fields may be preserved as a remnant of variousphenomenon such as, inflation, density fluctuations,reionization.
influence on structure formation

this talkgeneration and observation●magnetogenesis from cosmological perturbations
before recombination●observation of tiny cosmological magnetic fields
with pair echo from high-energy �-ray sources2. Magnetogenesis fromcosmological perturbations
KT, K. Ichiki, N. Sugiyama 05, 06, 07, 08
KT, T. Kobayashi, R. Maartens, T. Shiromizu, 07

cosmological perturbations
perturbation= deviation from homogeneous isotropic universe
・generated during inflation quantum mechanically→ density fluctuation, gravitational waves
・evolve linearly after inflation→ CMB anisotropy, structure formationprimordial fluctuations
observation
・CMB・galaxy distribution
theory・inflation(initial condition)
・cosmologicalperturbation theory(linear)

WMAP

magnetogenesis
magnetogenesis fromcosmological perturbations
before recombination
Hogan (2000)
Berezhiani & Dolgov (2004)
Matarrese et al. (2005)
Gopal & Sethi (2005)
KT et al. (2005, 2006, 2007, 2008)
Siegel & Fry (2006)
Hollenstein et al. (2008)
Maeda et al. (2009)

based on・cosmological perturbation
theory (nonlinear)・observational facts
・no physical assumption

basic idea
photons→ CMB

Thomsonscattering

baryonprotons
electrons
Coulomb
interaction

Thomson scattering→ deviation in motion
due to mass difference→ net electric charge densityand electric current→ magnetic fields

extensions to the conventional formalism
What do we need for magnetogenesis?
electric field and its rotationelectric field・Conventionally, baryons
・Separate treatment of p and e is necessary.
rotational part・No rotational part at the linear order・generated by nonlinear effectLinear order is sufficient for CMB
but insufficient for B.
Two extensions are needed for magnetogenesis.

generalized Ohm’s law(special relativistic) EOMs for protons and electrons

Coulomb

generalized Ohm’s law“wind” of photons

Thomsonbehaviour of charge density
divergence of the generalized Ohm’s law
damped oscillation
with an external source

In cosmological timescale, plasma oscillation damps.
The equilibrium is nonzero due to the source.

electromagnetic properties of the early universe
E fieldproton

photonpressure

electron・electric current term is not important in Ohm’s law→ photon pressure balances with E field・current → (displacement current) + (B field)
・E and charge vanish when Thomson term disappear.
B and current do not because they are integral.

relative motion of baryons and photons
source for B field (neglect anisotropic stress)

equation for velocity differencetight coupling approximation

results

The source vanishes at the lowest order intight coupling approximation.
So B is second order in both tight coupling
and cosmological perturbation.
All electromagnetic quantities are expressedin terms of familiar quantities like first-order ��.

quantitative study
KT et al. (2006)
・derive the source term relativistically・numerically calculate the spectrum
contributed from (1st order) × (1st order),neglecting the vorticity (purely 2nd order)(The products of 1st-order quantities are easily
calculated with CMBFAST or CAMB. But thevorticity needs 2nd-order Boltzmann solver.)spectrum
comoving B（log B (G))

-20
-24
-28

assumedscale invariant
fluctuations

-32
-36
-40
-44
1Gpc

1Mpc

scale

1kpc

1pc

implication
comoving B（log B (G))-20-24

cutoff
at 100AU～ 10 -21 G-28-32prediction ofcosmological B～ 10 -30 G-36-40
-44
1Gpc

1Mpc

scale

This is a robust resultin the sense that
B is created fromfluctuations alreadymeasured (large scale).
1kpc

1pc

toward the complete spectrum
analytic approach・based on tight coupling approximation
・understand the physics of magnetogenesis
and confirm the results of numerical calculation・needs relativistic formalism including
anisotropic stress (KT. Maartens, Pitrou)
numerical approach・evaluate the spectrum
・confirm the validity of tight coupling approximation
・include vorticity (purely 2nd order)
These two approaches are necessary
to cross check and evaluate the complete spectrum.

summary of magnetogenesis
magnetogenesis from cosmological perturbations
・difference of motion of p and e
due to Thomson scattering
・two extensions: p-e system and nonlinear effect・B field is generated at 2nd order in bothtight coupling and cosmological perturbation
・B ～10-21 Gauss (preliminary)・prediction of cosmological magnetic fields

3. Observation of tiny
cosmic magnetic fields
KT, K. Ichiki, S. Inoue, K. Murase et al. 07, 08, 09

cosmological magnetic fields
mechanisms
cosmological perturbation (KT et al. 05, 06, 07, 08)
inflation (Turner & Widrow 88, Demozzi et al. 09)
phase transition (Hogan 83)
reionization (Langer et al. 03, 05)
quasar outflow (Furlanetto & Loeb 2001)
How can they be verified?
galaxy, cluster of galaxies→ amplification, no information on initial condition
void region→ Initial condition is preserved?

method
How can we probe tiny B fields in void region?
CMB・Faraday rotation→ current limit: B < 1nG→ hard to reach 10 -20 G
Plaga’s method (Plaga, 1994)
probe tiny B fields by delayed emission
from high-energy sources like GRB and blazar→ B = 10 -15 ～ 10-20 G→ currently the most effective method

extragalactic background light

EBLCIB�-ray absorption

optical depth

�-rays with energy > TeV
from cosmological sources
are absorbed.

Spectrum of Mkn501 (z=0.03)
observed by MAGIC.
Intrinsic spectrum
derived with a EBL model.

What happened tothe absorbed energy?

cascadeCMB

EBL (eV)inverseComptonγ-ray(TeV)

γ-ray(GeV)

e± pairγe ～ 10 6CMB

TeV γ-ray is transformed to many GeV γ-rays.
＊The direction changes by 1/γe in each interaction.

pair echo

Plaga 95
Cheng & Cheng 96
Dai & Lu 02
KT et al. 07, 08, 09

CMBIR

�-ray(TeV)�-ray(MeV)
GRB, AGNe± pairIC�-ray(GeV)

timedelaypair echo

delay time
The primary does
not have to be directed
toward us.

λγγλIC~ 1/ γ e~ 1/ γ eθDelay time is determined by the mean free pathand the deflection angle, which depend on the energy.pair echo with magnetic field
CMBIR

�-ray(TeV)±e pairIC

�-ray(GeV)�-ray(MeV)
B field
GRB, AGN

B fields increase the delay time.
The delay time has information on B.

characteristic numbers ①IR

 Eγ 
EIR = 0.1eV 1TeV −1CMB Eγ 
Epa = 0.6GeV 1TeV 2Eγ = 1TeV

 nIR λγγ = 2Mpc
−3 
 1cm −1

 Eγ λIC = 0.4Mpc
 1TeV −1−22E
 delay   B   − 20 ∆t B = 0.5 day  1GeV   10 G characteristic numbers ②
Eγ = 1TeV・TeV blazar
・no observation from GRB, but theoretically likely
 Eγ 
Epa = 0.6GeV 1TeV 

2・energy range for Fermi
・terrestrial Cherenkov telescopes are also useful−22E pa   B   − 20 ∆t B = 0.5 day  1GeV   10 G ・high-energy (low-energy) �-rays for large (small) B

characteristic numbers ③
 nIR λγγ = 2Mpc
−3 
 1cm −1・enough large for the primary to escape the host Eγ 
λIC = 0.4Mpc
 1TeV −1・interaction is local even combined with the above
We can probe B fields in void region in manycases. (Of course it depends on the configuration.)→ It is useful to probe cosmic magnetic fields.

ideal configuration
GRB・AGN～ 10Mpc
probe B here!

expected flux contourtime(sec)101010−2

 Epa   B   − 20 ∆t B = 0.5 day  1GeV   10 G 

52Spectrum at each time
contains information on B.

431GeV 10GeV100GeVenergysetup
primary GRB

CIB model“best fit”model(“low SFR” model)of Kneiske et al. 02, 04

pair echo spectrum

high energy
weak B→ decay fasterlight curve at 1 GeV & Fermi
Epa = 1 GeVFermi

light curve at 100 GeV & MAGIC
Epa = 100 GeV

observability of pair echo

Fermi

expected constraints on B
B
Faraday rotation-9

delay time
too long

CMB-15

too shortpair echo
-20
1Gpc

1Mpc

1kpc

1pc

100AU

summary of pair echo
・probe tiny B fields with pair echo fromdistant high-energy sources
・TeV �-ray+ CIB → TeV e pair+ CMB → GeV �-rays
・path is deflected by pair creation, IC, B fields→ induce time delay
・sensitive to 10-15 ～ 10-20 G
・GRB with z < 1・high-z GRB?

summary of this talkgeneration and observation of cosmic magnetic field
generation
・cosmological perturbation before recombination
・photons, protons, electrons, EM fields
・2nd order perturbation
・robust prediction
observation
・pair echo from GRBs and blazars
・time delay due to B field・observe tiny B fields in void region
・sensitive to 10-17 ～ 10-20 Gauss・probe early universe, reionization

comparison with afterglow
afterglow 10 53-54 erg

Pair echo would be hiddenin early phase by afterglow.
But afterglow tend to decay
faster.